pcbcgsolver.cxx

another source code for reduced basis

#include<stdio.h>
#include<math.h>
#include"PCBCGSolver.h"

#define EPS 1.0e-14

void PCBCGSolver::dsprsax(double sa[], unsigned long ija[], double x[], double b[], unsigned long n){
	
	unsigned long i,k;

	if (ija[1] != n+2) printf("dsprsax: mismatched vector and matrix");
	for (i=1;i<=n;i++) {
		b[i]=sa[i]*x[i];
		for (k=ija[i];k<=ija[i+1]-1;k++) b[i] += sa[k]*x[ija[k]];
	}
}
void PCBCGSolver::dsprstx(double sa[], unsigned long ija[], double x[], double b[], unsigned long n)
{
	
	unsigned long i,j,k;
	if (ija[1] != n+2) printf("mismatched vector and matrix in dsprstx");
	for (i=1;i<=n;i++) b[i]=sa[i]*x[i];
	for (i=1;i<=n;i++) {
		for (k=ija[i];k<=ija[i+1]-1;k++) {
			j=ija[k];
			b[j] += sa[k]*x[i];
		}
	}
}
void PCBCGSolver::asolve(unsigned long n, double b[], double x[], int itrnsp)
{
	unsigned long i;

	for(i=1;i<=n;i++) x[i]=(sa[i] != 0.0 ? b[i]/sa[i] : b[i]);
}
void PCBCGSolver::atimes(unsigned long n, double x[], double r[], int itrnsp)
{
  if (itrnsp) dsprstx(sa,ija,x,r,n);
  else dsprsax(sa,ija,x,r,n);
}
double PCBCGSolver::snrm(unsigned long n, double sx[], int itol)
{
	unsigned long i,isamax;
	double ans;

	if (itol <= 3) {
		ans = 0.0;
		for (i=1;i<=n;i++) ans += sx[i]*sx[i];
		return sqrt(ans);
	} else {
		isamax=1;
		for (i=1;i<=n;i++) {
			if (fabs(sx[i]) > fabs(sx[isamax])) isamax=i;
		}
		return fabs(sx[isamax]);
	}
}
void PCBCGSolver::linbcg(unsigned long n, double b[], double x[], int itol, double tol,
	int itmax, int *iter, double *err)
{
	
	
	
	
	unsigned long j;
	double ak,akden,bk,bkden,bknum,bnrm,dxnrm,xnrm,zm1nrm,znrm;
	double *p,*pp,*r,*rr,*z,*zz;

	p=new double[n+1];
	pp=new double[n+1];
	r=new double[n+1];
	rr=new double[n+1];
	z=new double[n+1];
	zz=new double[n+1];

	*iter=0;
	atimes(n,x,r,0);
	for (j=1;j<=n;j++) {
		r[j]=b[j]-r[j];
		rr[j]=r[j];
	}
	znrm=1.0;
	if (itol == 1) bnrm=snrm(n,b,itol);
	else if (itol == 2) {
		asolve(n,b,z,0);
		bnrm=snrm(n,z,itol);
	}
	else if (itol == 3 || itol == 4) {
		asolve(n,b,z,0);
		bnrm=snrm(n,z,itol);
		asolve(n,r,z,0);
		znrm=snrm(n,z,itol);
	} else printf("illegal itol in linbcg");
	asolve(n,r,z,0);
	while (*iter <= itmax) {
		++(*iter);
		zm1nrm=znrm;
		asolve(n,rr,zz,1);
		for (bknum=0.0,j=1;j<=n;j++) bknum += z[j]*rr[j];
		if (*iter == 1) {
			for (j=1;j<=n;j++) {
				p[j]=z[j];
				pp[j]=zz[j];
			}
		}
		else {
			bk=bknum/bkden;
			for (j=1;j<=n;j++) {
				p[j]=bk*p[j]+z[j];
				pp[j]=bk*pp[j]+zz[j];
			}
		}
		bkden=bknum;
		atimes(n,p,z,0);
		for (akden=0.0,j=1;j<=n;j++) akden += z[j]*pp[j];
		ak=bknum/akden;
		atimes(n,pp,zz,1);
		for (j=1;j<=n;j++) {
			x[j] += ak*p[j];
			r[j] -= ak*z[j];
			rr[j] -= ak*zz[j];
		}
		asolve(n,r,z,0);
		if (itol == 1 || itol == 2) {
			znrm=1.0;
			*err=snrm(n,r,itol)/bnrm;
		} else if (itol == 3 || itol == 4) {
			znrm=snrm(n,z,itol);
			if (fabs(zm1nrm-znrm) > EPS*znrm) {
				dxnrm=fabs(ak)*snrm(n,p,itol);
				*err=znrm/fabs(zm1nrm-znrm)*dxnrm;
			} else {
				*err=znrm/bnrm;
				continue;
			}
			xnrm=snrm(n,x,itol);
			if (*err <= 0.5*xnrm) *err /= xnrm;
			else {
				*err=znrm/bnrm;
				continue;
			}
		}
		//printf("iter=%4d err=%12.6f\n",*iter,*err);
	if (*err <= tol) break;
	}

	delete [] p;
	delete [] pp;
	delete [] r;
	delete [] rr;
	delete [] z;
	delete [] zz;
}
#undef EPS